The contact system on the $(m, \ell)$-jet spaces

J. Munoz, F. J. Muriel, J. Rodriguez

Address. J. Munoz and J. Rodriguez, Departamento de Matematicas, Univ. de Salamanca, Plaza de la Merced 1-4, 37008 Salamanca, SPAIN

F. J. Muriel, Departamento de Matematicas, Univ. de Extremadura, Avda. de la Universidad s/n, 10004 Caceres, SPAIN



Abstract. This paper is a continuation of \cite{MMR:98}, where we give a construction of the canonical Pfaff system $\Omega(M_m^\ell)$ on the space of $(m,\ell)$-velocities of a smooth manifold $M$. Here we show that the characteristic system of $\Omega(M_m^\ell)$ agrees with the Lie algebra of $\AUT$, the structure group of the principal fibre bundle ${\check M}_m^\ell\longrightarrow {\mathcal J}_m^\ell(M)$, hence it is projectable to an irreducible contact system on the space of $(m,\ell)$-jets ($=\ell$-th order contact elements of dimension $m$) of $M$. Furthermore, we translate to the language of Weil bundles the structure form of jet fibre bundles defined by Goldschmidt and Sternberg in \cite{Gol:Ste:73}.

AMSclassification. 58A20

Keywords. Near points, jets, contact elements, contact system, velocities